On the well-posedness of the damped time-harmonic Galbrun equation and\n the equations of stellar oscillations

2020/06/13 by Martin Halla, Halla, Martin, Thorsten Hohage +1
Engineering · Mathematics · Physics and Astronomy · #35Q35 #35Q85 #76Q05 #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2006.07658

openalex publication_date 2020/06/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the time-harmonic Galbrun equation describing the propagation of\nsound in the presence of a steady background flow. With additional rotational\nand gravitational terms these equations are also fundamental in helio- and\nasteroseismology as a model for stellar oscillations. For a simple damping\nmodel we prove well-posedness of these equations, i.e. uniqueness, existence,\nand stability of solutions under mild conditions on the parameters (essentially\nsubsonic flows). The main tool of our analysis is a generalized Helmholtz\ndecomposition.\n

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